from tools_algorithm import *


class Solution:
    def maximizeWin(self, prizePositions: List[int], k: int) -> int:
        cnt = Counter(prizePositions)
        keys = sorted(cnt.keys())
        c, l = 0, 0
        f = [0] * (len(keys) + 1)
        ans = 0
        for i, v in enumerate(keys):
            c += cnt.get(v)
            while keys[l] + k < v:
                c -= cnt.get(keys[l])
                l += 1
            f[i + 1] = max(f[i], c)
            ans = max(ans, c + f[l])
        return ans


class Solution:
    def maximizeWin(self, prizePositions: List[int], k: int) -> int:
        cnt = Counter(prizePositions)
        keys = sorted(cnt.keys())
        c, l = 0, 0
        ans = 0
        mx = 0
        q = deque()
        for v in keys:
            c += cnt.get(v)
            while keys[l] + k < v:
                c -= cnt.get(keys[l])
                l += 1
                mx = max(mx, q.popleft())
            q.append(c)
            ans = max(ans, c + mx)
        return ans


# class Solution:
#     def maximizeWin(self, prizePositions: List[int], k: int) -> int:
#         cnt = Counter(prizePositions)
#         keys = sorted(cnt.keys())
#         c, l = 0, 0
#         ans = 0
#         mx = 0
#         q = deque()
#         for i, v in enumerate(keys):
#             s = cnt.get(v)
#             c += s
#             while keys[l] + k < v:
#                 c -= cnt.get(keys[l])
#                 l += 1
#                 mx = q.popleft()
#             # print(list(q))
#             q.append(max(q[-1] if q else 0, c))
#             ans = max(ans, c + mx)
#         return ans


s = Solution()
print(
    s.maximizeWin(
        [
            885752020,
            885756956,
            885807567,
            885837743,
            885849450,
            885894531,
            885929312,
            885931662,
            886058747,
            886096971,
            886098826,
            886120215,
            886167102,
            886177838,
            886232776,
            886241031,
            886317479,
            886319136,
            886373787,
            886425727,
            886443885,
            886502351,
            886528719,
            886535215,
            886574039,
            886694251,
            886762584,
            886773426,
            886851074,
            886930648,
            886994977,
            887015963,
            887125310,
            887172809,
            887179116,
            887199570,
            887204341,
            887259587,
            887365552,
            887369051,
            887388776,
            887410802,
            887430459,
            887639522,
            887814793,
            887848113,
            887885779,
            887899803,
            887922670,
            887925062,
            887927740,
            887971712,
            887991599,
            888024510,
            888243760,
            888412144,
            888441363,
            888502940,
            888584827,
            888592967,
            888600329,
            888659678,
            888669167,
            888823550,
            888848241,
            888934798,
            889004387,
            889005122,
            889023885,
            889063783,
            889099179,
            889133952,
            889147323,
            889155008,
            889226960,
            889300563,
            889318442,
            889331082,
            889367599,
            889386482,
            889442314,
            889454347,
            889559593,
            889596842,
            889609538,
            889618399,
            889717143,
            889765571,
            889774902,
            889808753,
            889831804,
            889854902,
            889872341,
            889873977,
            889953507,
            890020487,
            890121488,
            890128004,
            890214509,
            890217040,
            890237124,
            890241467,
            890354356,
            890357664,
            890478911,
            890504023,
            890519526,
            890523404,
            890536167,
            890551394,
            890687973,
            890694979,
            890736459,
            890750311,
            890751891,
            890797648,
            890880095,
            890887592,
            890935346,
            890941951,
            890988758,
            890989303,
            891038158,
            891040619,
            891083710,
            891118452,
            891148823,
            891198421,
            891206147,
            891229171,
            891256198,
            891266698,
            891280594,
            891294330,
            891396115,
            891427135,
            891559939,
            891591606,
            891677971,
            891743304,
            891771621,
            891937736,
            892053301,
            892070749,
            892199049,
            892212910,
            892232351,
            892281898,
            892332295,
            892351921,
            892424027,
            892504898,
            892602753,
            892614793,
            892643121,
            892691659,
            892707482,
            892748391,
            892778295,
            892805275,
            892854149,
            892890917,
            892941223,
            892951872,
            892964249,
            893111214,
            893114456,
            893165501,
            893203480,
            893227798,
            893336889,
            893349306,
            893471654,
            893563639,
            893603924,
            893653251,
            893661583,
            893695841,
            893909062,
            893913990,
            893959740,
            894050390,
            894065170,
            894195066,
            894208740,
            894262982,
            894263921,
            894292677,
            894343226,
            894393267,
            894413940,
            894415595,
            894447171,
            894515583,
            894558271,
            894576980,
            894638350,
            894692046,
            894710518,
            894771749,
            894815685,
            894863384,
            894934988,
            894978618,
            894979220,
            895082052,
            895100380,
            895149432,
            895164985,
            895193712,
            895324160,
            895338164,
            895419047,
            895575054,
            895627695,
            895634795,
            895648728,
            895675173,
            895693733,
            895827822,
            895830238,
            895954063,
            895981360,
            895989961,
            896005111,
            896057976,
            896131778,
            896137527,
            896151511,
            896167880,
            896202337,
            896221722,
            896229153,
            896240871,
            896246029,
            896253564,
            896257536,
            896311684,
            896334011,
            896347083,
            896363352,
            896393975,
            896435687,
            896468487,
            896484101,
            896495175,
            896504657,
            896519376,
            896532916,
            896566321,
            896624755,
            896656491,
            896686290,
            896714973,
            896752164,
            896763868,
            896767885,
            896773908,
            896779834,
            896865966,
            896928558,
            896945836,
            896951207,
            897007668,
            897064841,
            897103899,
            897110002,
            897179773,
            897180491,
            897213842,
            897239881,
            897260677,
            897273770,
            897459365,
            897500381,
            897606938,
            897616752,
            897659799,
            897682854,
            897756148,
            897793043,
            897796327,
            897881832,
            897935928,
            897974183,
            898011569,
            898043140,
            898053569,
            898108818,
            898110700,
            898118802,
            898228260,
            898241784,
            898251713,
            898287826,
            898389877,
            898397527,
            898427016,
            898508934,
            898586522,
            898594921,
            898685371,
            898700830,
            898731039,
            898786339,
            898949398,
            899049118,
            899084985,
            899113667,
            899121589,
            899126650,
            899156102,
            899207726,
            899235729,
            899252228,
            899288938,
            899305933,
            899367011,
            899385109,
            899389743,
            899396959,
            899451940,
            899526199,
            899526480,
            899591287,
            899597678,
            899649922,
            899681211,
            899728171,
            899754770,
            899824849,
            899901082,
            899964042,
            900012605,
            900050742,
            900073302,
            900104936,
            900143586,
            900155157,
            900160895,
            900187010,
            900297482,
            900412219,
            900419723,
            900451263,
            900452095,
            900459023,
            900463060,
            900465811,
            900486904,
            900513936,
            900535028,
            900569281,
            900648948,
            900720309,
            900728518,
            900748601,
            900760827,
            900941853,
            900967362,
            901024593,
            901031803,
            901104362,
            901133402,
            901135278,
            901177644,
            901238628,
            901243357,
            901288919,
            901293431,
            901316603,
            901509450,
            901574581,
            901603032,
            901639345,
            901644220,
            901685278,
            901720934,
            901724800,
            901845006,
            901860154,
            901867797,
            901881290,
            901890263,
            901906482,
            901920157,
            902055632,
            902105996,
            902121503,
            902175964,
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            906257151,
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            906675716,
            906685872,
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            906880356,
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            907435781,
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            907528172,
            907563885,
            907621682,
            907629814,
            907686931,
            907780713,
            907806295,
            907819178,
            907845405,
            907908815,
            907963997,
            908001236,
            908010184,
            908059395,
            908114113,
            908303506,
            908332823,
            908500229,
            908528633,
            908595885,
            908743697,
            908800311,
            908804755,
            908875023,
            908896208,
            908950841,
            908955176,
            908998088,
            909011529,
            909028916,
            909029646,
            909085990,
            909121615,
            909163088,
            909175626,
            909211868,
            909247771,
            909261964,
            909322461,
            909396742,
            909403653,
            909494232,
            909531021,
            909538065,
            909603367,
            909790410,
            909821552,
            909856262,
            909856569,
            910045065,
            910177718,
            910183200,
            910241686,
            910286100,
            910325394,
            910328516,
            910359825,
            910365627,
            910382755,
            910383375,
            910441300,
            910536852,
            910568439,
            910576859,
            910580280,
            910611777,
            910634826,
            910636932,
            910654955,
            910706955,
            910709267,
            910723867,
            910778780,
            910789721,
            910827418,
            910846822,
            910886981,
            910951879,
            911125706,
            911141103,
            911181933,
            911229901,
            911271813,
            911349009,
            911420119,
            911493270,
            911494711,
            911499380,
            911533401,
            911539361,
            911550421,
            911561281,
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            911758304,
            911782600,
            911803087,
            911885174,
            911902866,
            911930465,
            911931497,
            911945327,
            911958742,
            912067782,
            912072503,
            912304868,
            912341806,
            912403978,
            912427565,
            912469547,
            912475235,
            912544600,
            912562406,
            912624366,
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            912771019,
            912797291,
            912809177,
            912859513,
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            914906176,
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            914975937,
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            915276506,
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            915375879,
            915491292,
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            915742359,
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            915802131,
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            915912165,
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            915995644,
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            916364012,
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            918168825,
            918208645,
            918222738,
            918279297,
            918319040,
            918376560,
            918388917,
            918495081,
            918532204,
            918564598,
            918578214,
            918823248,
            918853926,
            918881773,
            918897735,
            918901473,
            918932699,
            918949514,
            919003868,
            919060418,
            919077274,
            919149520,
            919157064,
            919210036,
            919295204,
            919633663,
            919669405,
            919679624,
            919724392,
            919801564,
            919842866,
            919941113,
            919980509,
            920026040,
            920089401,
            920134226,
            920143666,
            920241874,
            920273011,
            920355813,
            920402440,
            920428298,
            920485582,
            920524750,
            920642004,
            920731036,
            920743704,
            920783584,
            920830353,
            920839454,
            920887451,
            920899647,
            921013584,
            921017295,
            921151550,
            921184422,
            921313976,
            921323065,
            921323317,
            921417645,
            921496452,
            921511164,
            921541145,
            921552665,
            921577330,
            921591344,
            921680399,
            921691335,
            921738142,
            921745633,
            921802419,
            921820715,
            921910904,
            921930737,
            921938297,
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            922008681,
            922010884,
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            922053273,
            922113416,
            922116871,
            922150578,
            922156302,
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            922261552,
            922366770,
            922401895,
            922420269,
            922433019,
            922454995,
            922484134,
            922597648,
            922632980,
            922637038,
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            922672101,
            922708707,
            922754099,
            922867483,
            922924740,
            923078411,
            923131023,
            923159217,
            923209836,
            923216018,
            923256689,
            923256693,
            923297415,
            923374286,
            923386158,
            923448786,
            923476278,
            923585411,
            923631661,
            923641967,
            923664695,
            923665684,
            923669094,
            923691628,
            923825156,
            923864819,
            923896181,
            923920623,
            923938199,
            923967993,
            924038915,
            924074350,
            924099618,
            924207604,
            924208362,
            924211720,
            924234752,
            924287686,
            924292391,
            924381075,
            924428356,
            924469530,
            924498593,
            924520708,
            924531996,
            924581108,
            924599480,
            924622322,
            924629272,
            924677888,
            924684365,
            924688805,
            924748139,
            924766845,
            924775355,
            924854505,
            924947297,
            924948016,
            924995209,
            925029013,
            925057457,
            925194276,
            925291215,
            925378480,
            925452038,
            925485646,
            925584551,
            925589920,
            925674618,
            925678734,
            925679768,
            925724537,
            925732689,
            925768233,
            925770116,
            925836603,
            925927259,
            925995628,
            926079388,
            926096820,
            926150415,
            926152577,
            926197922,
            926322413,
            926339121,
            926349035,
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